Given the family of lines, a (3x + 4y + 6)b(x+y+2)0. The line of the f

1.	Given the family of lines, a (3x + 4y + 6)b(x+y+2)0. The line of the family situatedat the greatest distance from the point P(2, 3)has equation:(2) 5x + 3y 10 0(3) 15x + 8y + 30 0(4) 4x- 3y +8 0
Answer» Find the common point of intersection of this family of lines. Here it is (-2,0). Now, given point is (2,3). Equation of line passing through both the points is : 3x + 6 =4y. You actually only need the slope of this line which is : 3/4 Line perpendicular to this line passing through the common point will be at the greatest distance. Slope of the required line: -4/3 Equation of the line :-4/3{x-(-2)} = y-0 After solving, equation is : 4x + 3y + 8 =0. The answer is Option 1.

Given the family of lines, a (3x + 4y + 6)b(x+y+2)0. The line of the family situatedat the greatest distance from the point P(2, 3)has equation:(2) 5x + 3y 10 0(3) 15x + 8y + 30 0(4) 4x- 3y +8 0

Answer»

Find the common point of intersection of this family of lines.

Here it is (-2,0). Now, given point is (2,3).

Equation of line passing through both the points is : 3x + 6 =4y.

You actually only need the slope of this line which is : 3/4

Line perpendicular to this line passing through the common point will be at the greatest distance. Slope of the required line: -4/3

Equation of the line :-4/3{x-(-2)} = y-0

After solving, equation is : 4x + 3y + 8 =0.

The answer is Option 1.